[kubuntu] Auto turn on with UPS ?

I have a computer that runs Kubuntu 14. I use it solely for transmitting my weather station info to Weather Underground. It takes in the info from the weather station (via RS232) and sends it on via the inteet.
Lately we have had a number of power outages because of storms, some outages have lasted many hours or a day or longer. The problem is that I am not always there to start things back up and may be gone for days before I can get back. During that time the computer is off.
I have the computer set to power on when electricity is restored, but lately it seems to be confused when trying to power up and hangs on the grub display even though there is no other OS on the hard drive.

I just bought a UPS (1350) which will probably last several hours. It will safely power down the computer when the power goes out, but the problem is how to tu the computer back on when the power is restored without me having to physically push the on button.

I'm trying to get some ideas for how to resolve this. Currently I am away from home and the power has come back on but I'm not there to restart the computer.

Ideas?